Zeros of Jensen polynomials and asymptotics for the Riemann xi function

Abstract

The classical criterion of Jensen for the Riemann hypothesis is that all of the associated Jensen polynomials have only real zeros. We find a new version of this criterion, using linear combinations of Hermite polynomials, and show that this condition holds in many cases. Detailed asymptotic expansions are given for the required Taylor coefficients of the xi function at $1/2$ as well as related quantities. These results build on those in the recent paper of Griffin, Ono, Rolen and Zagier.

22 pages. In version 2 typos fixed and references added. To appear in Research in the Mathematical Sciences

References in corpus (3)

• Jensen Polynomials for the Riemann Xi Function
• Orthogonal polynomial expansions for the Riemann xi function
• The Riemann hypothesis is true up to $3\cdot 10^{12}$

Cited by in corpus (1)

• Jensen Polynomials for the Riemann Xi Function